Rescue workers dived deep inside a flooded Thai cave for a second straight day Monday in a treacherous bid to save a trapped group of young footballers, with the mission chief promising more "good news" after four of the 13 were saved.

Sunday's surprisingly quick extraction of the initial batch of four, who were guided out of a network of flooded tunnels by elite divers, fuelled optimism that the others would also be quickly rescued.

"All the equipment is ready. Oxygen bottles are ready," rescue operations chief Narongsak Osottanakorn told reporters on Monday afternoon after announcing the second phase of the rescue bid had begun.

"In the next few hours we will have good news."

Thais have been fixated on the crisis, hoping desperately for the safe return of the 12 boys and their 25-year-old football coach, after they ventured into the Tham Luang cave complex after practice and became trapped by rising waters on June 23.

The saga has also dominated global headlines, with the team spending nine days unaccounted for inside the cave, before British divers found the emaciated and dishevelled group huddling on a muddy bank above the flooding.

Authorities then struggled to determine the best way to save the "Wild Boar" football team, with the group stuck on a shelf more than four kilometres (2.5 miles) inside the cave in pitch darkness.

Among the ideas were drilling an escape route through the mountain, and leaving them for months until the monsoon season ended and the flooding subsided.

But with oxygen levels inside dropping to dangerous lows and the prospect of heavy rains flooding the area completely, authorities decided they had to move quickly and take the group out through the water-filled tunnels.

Dozens of foreign divers and other experts from around the world were brought to help the rescue effort, working alongside Thai Navy SEALs.

Deadly dangers
Narongsak described Sunday's initial rescue bid as "D-Day" when it was launched, and there were fears that any one of many potential pitfalls could prove deadly.

Among these were that none of the boys had scuba diving experience, and that they could easily panic while swimming underwater in darkness.

The death of a former Thai Navy SEAL diver who ran out of oxygen in the cave on Friday underscored the danger of the journey even for professionals.

But after the first four emerged late on Sunday afternoon, hopes began to rise of a fairytale ending to the ordeal.

Narongsak on Sunday described their journey out, escorted by elite divers, as "smooth".

Thai premier Prayut Chan-O-Cha was also due to visit the rescue operation late on Monday.

Still, for the relatives of the Wild Boar team members, an agonising wait continued.

"I am still waiting here at the cave, keeping my fingers crossed to see whether my son will be one of those to come out today," Supaluk Sompiengjai, mother of Pheeraphat -- known by his nickname "Night" -- told AFP on Monday morning.

"We heard four boys are out but we do not know who they are. Many parents are still here waiting. None of us has been informed of anything."

And although the four had been rescued, there were concerns they may have contracted an illness while in the cave, Narongsak said on Monday.

"They (the four) will be kept away from their parents for a while because we are concerned about infections," Narongsak said.

And rain could still re-emerge as a threat, particularly if there are complications that could delay the extraction further.

Weather forecasters warned heavy rain could hit the area on Monday afternoon and continue through the week.

Authorities have repeatedly said the rain could re-flood crucial parts of the cave complex that have been drained and make the escape route much harder or even impossible to navigate.